Epidemic Model with Isolation in Multilayer Networks
L G Alvarez Zuzek1, H E Stanley2, L A Braunstein3
1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET), Deán Funes 3350, 7600 Mar del Plata, Argentina.
Abstract:
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network, and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.
Insights
Implementing isolation in disease modeling significantly raises the epidemic threshold. The Susceptible-Infected-Isolated-Recovered (SIIR) model demonstrates that quarantining infected individuals effectively reduces disease spread, preventing epidemics.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- The Susceptible-Infected-Recovered (SIR) model is widely used for airborne disease simulation.
- Existing multilayer network models often neglect the crucial factor of infected individual isolation.
- This oversight limits the accuracy of disease propagation predictions.
Purpose of the Study:
- To introduce and analyze the Susceptible-Infected-Isolated-Recovered (SIIR) model in a two-layer network.
- To quantify the impact of quarantining infected individuals on epidemic thresholds.
- To investigate the influence of isolation duration and intensity on disease spread.
Main Methods:
- Development of the SIIR model incorporating an isolation parameter (w) and isolation period (tw).
- Application of link percolation theory to determine critical epidemic thresholds.
- Simulation of the SIIR model to validate theoretical findings.
Main Results:
- Isolation significantly increases the critical epidemic threshold, reducing disease transmissibility.
- The threshold escalates with increased isolation parameter (w) and duration (tw).
- A maximum isolation period exists, beyond which a critical 'w' can prevent epidemics entirely.
Conclusions:
- Quarantining infected individuals is a highly effective strategy for controlling airborne disease spread in multilayer networks.
- The SIIR model provides a more realistic framework for understanding epidemic dynamics than traditional SIR models.
- Strategic implementation of isolation measures can prevent widespread outbreaks.
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